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<p><i>We consider a class of Lévy processes that includes the symmetric</i><InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7975_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-<i>stable processes for</i> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7975_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \in (1,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. <i>Using these processes, we construct a family of stochastic operators and show that this family approximates the resolvent of the fractional differential operator of order</i> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7975_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. <i>Bibliography:</i>5 <i>titles</i>.</p>

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PROBABILISTIC REPRESENTATION FOR THE RESOLVENT OF A FRACTIONAL DIFFERENTIAL OPERATOR

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • T. E. Abildaev

摘要

We consider a class of Lévy processes that includes the symmetric \(\alpha \) α -stable processes for \(\alpha \in (1,2)\) α ∈ ( 1 , 2 ) . Using these processes, we construct a family of stochastic operators and show that this family approximates the resolvent of the fractional differential operator of order \(\alpha \) α . Bibliography:5 titles.